THEOREM 10.21 Root Test Let Ea, be an infinite series, and let p = lim V]a. 1. If p < 1, the series converges absolutely, and therefore it converges (by Theorem 10.19). 2. If p > 1 (including p = ∞), the series diverges. 3. If p 1, the test is inconclusive. k=1
THEOREM 10.21 Root Test Let Ea, be an infinite series, and let p = lim V]a. 1. If p < 1, the series converges absolutely, and therefore it converges (by Theorem 10.19). 2. If p > 1 (including p = ∞), the series diverges. 3. If p 1, the test is inconclusive. k=1
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Use the Ratio Test or the Root Test to determine the values of x for which the series converges.
![THEOREM 10.21
Root Test
Let Ea, be an infinite series, and let p = lim V]a.
1. If p < 1, the series converges absolutely, and therefore it converges
(by Theorem 10.19).
2. If p > 1 (including p = ∞), the series diverges.
3. If p
1, the test is inconclusive.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45853372-babe-4d35-8c29-069a987c5c76%2F35205aeb-7cea-4433-9198-a87f5d5a56b8%2F4m20k9d.png&w=3840&q=75)
Transcribed Image Text:THEOREM 10.21
Root Test
Let Ea, be an infinite series, and let p = lim V]a.
1. If p < 1, the series converges absolutely, and therefore it converges
(by Theorem 10.19).
2. If p > 1 (including p = ∞), the series diverges.
3. If p
1, the test is inconclusive.
Transcribed Image Text:k=1
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